A050246 -id:A050246 - cp's OEIS frontend

A118848 Number of minutes past midnight represented by A050246(n).

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 63, 67, 69, 73, 87, 91, 97, 99, 109, 111, 117, 131, 143, 147, 149, 153, 159, 161, 171, 177, 187, 191, 193, 197, 211, 217, 227, 229, 233, 239, 241, 249, 259, 261, 271, 273, 279, 283, 289, 297

Offset: 1

Carl R. White, May 01 2006

Prime members of this sequence can be found in A118850.

Nathaniel Johnston, Table of n, a(n) for n = 1..211 (full sequence)

Cf. A050246, A118849, A118850.

for h from 0 to 23 do for m from 0 to 59 do if(isprime(100*h+m))then printf("%d, ", 60*h+m): fi: od: od: # Nathaniel Johnston, May 17 2011

a(n) = A050246(n) - floor(A050246(n)/100)*40.

A118849 Digital clock primes such that the number of minutes past midnight is also prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 101, 107, 113, 137, 149, 211, 229, 311, 313, 317, 331, 347, 349, 353, 359, 401, 431, 443, 547, 607, 613, 619, 641, 659, 701, 719, 743, 811, 823, 829, 907, 929, 937, 947, 953, 1013, 1019, 1031, 1117

Offset: 1

Carl R. White, May 01 2006

The number of minutes past midnight represented by each of the times here can be found in A118850.

Nathaniel Johnston, Table of n, a(n) for n = 1..83 (full sequence)

Cf. A050246, A118848, A118850.

for h from 0 to 23 do for m from 0 to 59 do t:=100*h+m: if(isprime(60*h+m) and isprime(t))then printf("%d, ", t): fi: od: od: # Nathaniel Johnston, May 17 2011

a(n) = A118850(n) + floor(A118850(n)/60)*40.

A118850 Number of minutes past midnight represented by A118849(n).

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 73, 97, 109, 131, 149, 191, 193, 197, 211, 227, 229, 233, 239, 241, 271, 283, 347, 367, 373, 379, 401, 419, 421, 439, 463, 491, 503, 509, 547, 569, 577, 587, 593, 613, 619, 631, 677

Offset: 1

Carl R. White, May 01 2006

Prime members of A118848.

Nathaniel Johnston, Table of n, a(n) for n = 1..83 (full sequence)

Cf. A050246, A118848, A118849.

for h from 0 to 23 do for m from 0 to 59 do t:=60*h+m: if(isprime(100*h+m) and isprime(t))then printf("%d, ", t): fi: od: od: # Nathaniel Johnston, May 17 2011

a(n) = A118849(n) - floor(A118849(n)/100)*40.

A229106 Prime time display in hours, minutes, seconds on a six-digit 24-hour digital clock.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 211, 223, 227, 229, 233, 239, 241, 251, 257, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 401, 409, 419, 421, 431, 433, 439, 443

Offset: 1

Shyam Sunder Gupta, Sep 13 2013

Leading zeros are ignored, so the term a(3) = 5, for example, corresponds to the display 00:00:05. Sequence has 7669 entries. The first 211 terms are the same as in A050246.

			109 is in the sequence because it is prime and display the time as 00:01:09.

Shyam Sunder Gupta, Table of n, a(n) for n = 1..7669 (complete sequence)

Cf. A050246 (primes displayed on a 4-digit clock).

Select[Flatten[Table[10000*hr + 100*mnt + sec, {hr, 0, 23}, {mnt, 0, 59}, {sec, 0, 59}]], PrimeQ]

A159911 Prime times: primes of the form HMM with primes H, MM, 0

Original entry on oeis.org

211, 223, 229, 241, 307, 311, 313, 317, 331, 337, 347, 353, 359, 503, 523, 541, 547, 719, 743, 1103, 1117, 1123, 1129, 1153, 1303, 1307, 1319, 1723, 1741, 1747, 1753, 1759, 1907, 1913, 1931, 2311, 2341, 2347

Offset: 1

M. F. Hasler, May 01 2009

Suggested by E. Angelini, cf. link.

E. Angelini, in "Les membres de ce groupe forment un nombre premier", April 30, 2009.

See also A050246 and A229106, where H and MM (and SS) do not need to be prime.

Select[Flatten[Table[FromDigits[Join[IntegerDigits[h],PadLeft[ IntegerDigits[ m],2]]],{h,Prime[Range[9]]},{m,Prime[Range[ 17]]}]],PrimeQ] (* Harvey P. Dale, Mar 27 2022 *)

forprime( h=0,24, forprime( m=0,60, isprime(100*h+m) & print1(100*h+m,", ")))

A295000 Prime time primes (of the form HMMSS with primes H < 24 and MM, SS < 60) such that the corresponding number of seconds after midnight is also prime.

Original entry on oeis.org

20231, 20297, 20353, 20507, 20719, 20753, 20771, 21107, 21313, 21379, 21713, 21767, 21773, 21929, 21937, 22343, 22367, 22397, 22961, 22973, 23131, 23143, 23167, 23173, 23197, 23719, 23741, 23743, 23747, 23753, 24137, 24179, 24337, 24359, 24371, 24379

Offset: 1

M. F. Hasler, Jan 15 2018

Could be called "super prime time primes": all of H, MM, SS, HMMSS (6-digit clock display) and H*3600 + MM*60 + SS (seconds after midnight) are prime.
This sequence lists the prime time primes A295013 for which the number of seconds A295003 is prime. These are also the times HMMSS (obtained through A055643) which correspond to the subset A295002 of primes in A295003.
Sequence A295002 lists the number of seconds after midnight corresponding to the "prime times" = 6-digit clock displays listed here.
Sequences A295003 and A295004 list the number of seconds after midnight corresponding to the prime time primes A295013 and prime time numbers A295014, i.e., primes and all numbers of the form HMMSS where H < 24 and MM, SS < 60 are prime.

			The smallest prime of the form HMMSS, with H, MM, SS and H*3600 + MM*60 + SS also prime, is a(1) = 20231, corresponding to a prime number A295002(1) = H*3600 + MM*60 + SS = 7351 (the first prime in A295003) of seconds after midnight.

M. F. Hasler, Table of n, a(n) for n = 1..404 (complete sequence).

Cf. A295002, A295003, A295013, A295011, A295004, A295014; A050246, A159911, A229106; A118848, A118849, A118850; A055643, A292579.

apply( A055643, A295002) /* or */ select( p->isprime(A292579(p)), A295013)

a(n) = A055643(A295002(n)) ; A295000 = { A295013(k) | A295003(k) is prime }.

A295011 Numbers of the form HMMSS with primes H < 24 and MM, SS < 60, for which the number of seconds after midnight, 3600H+60MM+SS, is also prime.

Original entry on oeis.org

20211, 20213, 20229, 20231, 20313, 20331, 20337, 20353, 20507, 20517, 20523, 20529, 20537, 20541, 20547, 20559, 20719, 20723, 20729, 20753, 21107, 21113, 21117, 21119, 21123, 21141, 21147, 21159, 21313, 21329, 21331, 21337, 21359, 21711, 21713, 21717

Offset: 1

M. F. Hasler, Jan 16 2018

Subsequence of A295014 (prime time numbers) for which the corresponding number of seconds after midnight (A295004) is also prime.

The "super prime time primes" A295000 are the primes within this sequence.

			Construct all numbers of the form concat(H,MM,SS) where H < 24 and MM, SS < 60 are primes. These start 2:02:02, 2:02:03, 2:02:03, ... (without ":"s), this is A295014. The corresponding number of seconds after midnight is A292579(HMMSS) = 3600*H + 60*MM + SS. These numbers are listed in A295004. The first prime in that sequence is 7331 = A292579(20211), i.e., the first H:MM:SS for which that number of seconds is prime is 2:02:11, whence a(1) = 20211.

M. F. Hasler, Table of n, a(n) for n = 1..770 (complete sequence).

Cf. A295014, A295004, A295000, A295002, A295013, A295003; A050246, A159911, A229106; A118848, A118849, A118850.

With[{s = Prime@ Range@ PrimePi@ 60}, FromDigits@ Flatten[PadLeft[IntegerDigits[#], 2] & /@ #] & /@ Select[Tuples@ {TakeWhile[s, # < 24 &], s, s}, PrimeQ@ NumberCompose[{#1, #2, #3}, {3600, 60, 1}] & @@ # &]] (* Michael De Vlieger, Jan 21 2018 *)

select( t->isprime(A292579(t)), A295014)

A295013 Prime time primes on 6-digit clocks, second definition: primes of the form HMMSS where H, MM, SS are primes, H < 24, MM and SS < 60.

Original entry on oeis.org

20219, 20231, 20261, 20297, 20323, 20341, 20347, 20353, 20359, 20389, 20507, 20543, 20707, 20717, 20719, 20731, 20743, 20747, 20753, 20759, 20771, 20773, 20789, 21107, 21143, 21179, 21313, 21317, 21319, 21323, 21341, 21347, 21379, 21383, 21397, 21713

Offset: 1

M. F. Hasler, Jan 09 2018

A subsequence and variant of A229106, where the individual digit groups are not required to be primes. Also a subsequence (namely, the prime terms) of A295014, where H, MM and SS must be primes, but not the concatenation HMMSS.

See A295000 for the subsequence of terms for which the number of seconds after midnight (3600*H + 60*MM + SS, listed in A295003) is also prime.

M. F. Hasler, Table of n, a(n) for n = 1..1211 (complete sequence).

Cf. A050246, A159911, A229106; A118848, A118849, A118850.

Cf. A295014, A295003, A295011, A295000, A295002.

With[{s = Prime@ Range@ PrimePi@ 60}, Select[FromDigits@ Flatten[PadLeft[IntegerDigits[#], 2] & /@ #] & /@ Tuples@ {TakeWhile[s, # < 24 &], s, s}, PrimeQ]] (* Michael De Vlieger, Jan 21 2018 *)

is_A295013(n)=apply(isprime,digits(n,100))==[1,1,1]&&n<24e4&&isprime(n)
A295013 = select( is_A295013, primes([20000,240000]))

A295014 Prime time numbers on 6-digit clocks: numbers of the form HMMSS where H, MM, SS are primes, H < 24, MM and SS < 60.

Original entry on oeis.org

20202, 20203, 20205, 20207, 20211, 20213, 20217, 20219, 20223, 20229, 20231, 20237, 20241, 20243, 20247, 20253, 20259, 20302, 20303, 20305, 20307, 20311, 20313, 20317, 20319, 20323, 20329, 20331, 20337, 20341, 20343, 20347, 20353, 20359, 20502, 20503

Offset: 1

M. F. Hasler, Jan 09 2018

The primes in this sequence form the subsequence A295013, a variant and subsequence of A229106, where only the concatenation HMMSS but not the individual digit groups are required to be primes. See also A050246 and A159911 for 4-digit clock variants.

See A295011 for the subsequence of terms for which the number of seconds after midnight (3600*H + 60*MM + SS, given in A295004) is prime, and A295000 for the subsequence of primes therein.

M. F. Hasler, Table of n, a(n) for n = 1..2601 (complete sequence).

Cf. A295013, A050246, A159911, A229106.

With[{s = Prime@ Range@ PrimePi@ 60}, FromDigits@ Flatten[PadLeft[IntegerDigits[#], 2] & /@ #] & /@ Tuples@ {TakeWhile[s, # < 24 &], s, s}] (* Michael De Vlieger, Jan 21 2018 *)

is_A295014(n)=apply(isprime,digits(n,100))==[1,1,1]&&n<24e4
A295014 = select( is_A295014, [20000,240000])
/* alternatively */ A295014=List(); forprime(h=0,24,forprime(m=0,60,forprime(s=0,60,listput(A295014,(h*100+m)*100+s))))

A295002 Primes in A295003, the number of seconds after midnight corresponding to prime time primes A295013 (primes of the form HMMSS with primes H < 24 and MM, SS < 60).

Original entry on oeis.org

7351, 7417, 7433, 7507, 7639, 7673, 7691, 7867, 7993, 8059, 8233, 8287, 8293, 8369, 8377, 8623, 8647, 8677, 9001, 9013, 9091, 9103, 9127, 9133, 9157, 9439, 9461, 9463, 9467, 9473, 9697, 9739, 9817, 9839, 9851, 9859, 10453, 10753, 10771, 10837, 10867, 10949

Offset: 1

M. F. Hasler, Jan 15 2018

See A295000(n) = A055643(a(n)) for the corresponding "prime time primes", i.e., 6-digit clock displays. Reciprocally, the number of seconds given here is obtained through A292579 from the "super prime time primes" A295000.

M. F. Hasler, Table of n, a(n) for n = 1..404 (complete sequence).

Cf. A295000, A295003, A295013, A295011, A295014, A295004; A050246, A159911, A229106; A118848, A118849, A118850.

select( isprime, A295003) /* or */ apply(A292579,A295000)

a(n) = A292579(A295000(n))

cp's OEIS Frontend

A118848 Number of minutes past midnight represented by A050246(n).

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A118849 Digital clock primes such that the number of minutes past midnight is also prime.

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A118850 Number of minutes past midnight represented by A118849(n).

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A229106 Prime time display in hours, minutes, seconds on a six-digit 24-hour digital clock.

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A159911 Prime times: primes of the form HMM with primes H, MM, 0

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A295000 Prime time primes (of the form HMMSS with primes H < 24 and MM, SS < 60) such that the corresponding number of seconds after midnight is also prime.

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A295011 Numbers of the form HMMSS with primes H < 24 and MM, SS < 60, for which the number of seconds after midnight, 3600*H+60*MM+SS, is also prime.

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A295013 Prime time primes on 6-digit clocks, second definition: primes of the form HMMSS where H, MM, SS are primes, H < 24, MM and SS < 60.

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A295011 Numbers of the form HMMSS with primes H < 24 and MM, SS < 60, for which the number of seconds after midnight, 3600H+60MM+SS, is also prime.